In DSM IC designs, the coupling capacitance between adjacent nets has become a dominant component as taller and narrower wires are placed closer to each other. The coupling capacitance not only leads to excessive signal delays, but also causes potential logic malfunctions. The problem with such malfunctions is serious for designs with higher clock frequencies, lower supply voltages, and usage of dynamic logic since they have lower noise margin.
To design noise immune integrated circuits, an accurate yet efficient crosstalk noise model is needed to guide layout optimization at various stages. A number of researchers have worked towards developing simple but reasonably accurate crosstalk noise models suitable for layout optimizations. By solving telegraph equations directly analytical formula for peak noise amplitude for capacitively coupled bus lines were obtained. See T. Sakurai, “Closed-form Expressions for Interconnection Delay, Coupling, and Crosstalk in VLSIs,” IEEE Trans. on Electron Devices, vol. 40, pp. 118–124, 1993, and H. Kawaguchi and T. Sakurai, “Delay and Noise Formulas for Capacitively Coupled Distributed RC Lines,” in Proc. Asia and South Pacific Design Automation Conf., pp. 35–43, 1998. However, their approaches can only handle a fully coupled bus structure and cannot be used in general on-chip noise estimation for partially coupled line or general RC trees.
In A. Vittal & M. Marek-Sadowska, “Crosstalk Reduction for VLSI,” IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 16, pp. 290–98, 1997, each aggressor and victim net are modeled by an L-type RC circuit and a closed-form expression is obtained for both peak noise upper bound and noise-over-time integral. It showed much improvement on the pure charge sharing model. However, the modeling assumed a step input for the aggressor net. Subsequently, this model was extended to consider a saturated ramp input or a Pi-type lumped RC circuit. See S. Nakagawa, D. M. Sylvester, J. McBride, & S. -Y. Oh, “On-chip Cross Talk Noise Model for Deep-submicrometer ULSI Interconnect,” Hewlett-Packard Journal, vol. 49, pp. 39–45, August 1998.
In T. Stohr, M. Alt, A. Hetzel, and J. Koehl, “Analysis, Reduction and Avoidance of Crosstalk on VLSI Chips,” Proc. Int. Symp. on Physical Design, pp. 211–18, April 1998, an empirical pattern-based noise metric is obtained by using different coupling factors for different geometric and circuitry patterns. One problem with this approach is that the coupling factor is very much technology dependent.
Most of the models discussed above do not consider the distributed nature of an RC network, which is needed in DSM designs.
In A. Devgan, “Efficient Coupled Noise Estimation for On-chip Interconnects,” in Proc. Int. Conf. on Computer Aided Design, pp. 147–153, 1997, an Elmore-delay like peak noise model was disclosed for general RC trees in the manner exactly like the Elmore delay, which guarantees to be an upper bound. However, the model assumed an infinite (non-saturated) ramp input. Therefore, it tends to over-estimate the peak noise, especially for large victim nets, and small aggressor slews, which are very likely in DSM. In fact, the peak noise obtained from this model could even be larger than the supply voltage. Recent work in A. Vittal, L. Chen, M. Marek-Sadowska, K. -P. Wang, and S. Yang, “Crosstalk in VLSI Interconnections,” in IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 18, no. 2, pp. 1817–24, 1999, was shown to handle distributed networks and saturated ramp input. Even so, their model often gives larger errors when the aggressor slew is relatively large and leads to 100% over estimation compared to the Devgan model referred to above.
Thus, most previous crosstalk models used either over-simplified lumped RC model or unrealistic assumption (e.g., infinite ramp voltage input for aggressor net). Thus, they either underestimate or overestimate peak crosstalk noise significantly. In addition, most of these models only focused on the peak noise, while ignoring the crosstalk noise width modeling.